Marcus drew a scale drawing of the rectangular park in his neighborhood. on his drawing, the length of the park is 8 inches and the width of the park is 6 inches. the key on his drawing shows 1 inch=20 feet. what is the actual area of the park?

General rules or principles that are stated mathematically are known as mathematical theorems.

A theorem is a statement or proposition in mathematics that can be proved using logic and previously established facts or principles. It is a statement that has been shown to be true through a logical and rigorous argument. A theorem is considered to be an important and fundamental concept in mathematics and plays a key role in the development and advancement of the subject. Many famous theorems, such as the Pythagorean Theorem and the Fundamental Theorem of Calculus, have had a profound impact on mathematics and other fields of science.

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Answer:

(18, -14), 7

Step-by-step explanation:

y - (y-intercept) = slope (x - (x-intercept))

The equation of the line passing through the points (-1, 5) and (1, -5) is y = -5x.

The collection of points that make up a line in a coordinate system are represented algebraically by a line's equation. The many locations that make up a line on a coordinate axis are denoted by the letters (x, y), and the relationship between x and y results in an algebraic equation that is known as an equation of a line. We can determine whether a given point falls on a line using the equation of any line.

We can use the point-slope form of the equation of a line to solve this problem, which is:

y - y₁ = m(x - x₁)

where:

m = slope of the line

(x₁, y₁) = coordinates of one of the points on the line

First, let's find the slope (m) of the line using the two given points:

m = (y₂ - y₁) / (x₂ - x₁)

m = (-5 - 5) / (1 - (-1))

m = -10 / 2

m = -5

Now we can use one of the points, say (-1, 5), and the slope (-5) to write the equation of the line:

y - 5 = -5(x - (-1))

Simplifying and rearranging the equation:

y - 5 = -5x - 5

y = -5x + 0

Therefore, the equation of the line passing through the points (-1, 5) and (1, -5) is y = -5x.

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a.  the transition matrix P from {u, u2} to {e1, e2} is

P = [u u2]e = | 3 3 |

| 1 -1 |

b.)

the matrix representation of L with respect to {u, u2} is

[L]u = | 0 -3 |

|-4 -3 |

We must determine the coordinates of the basis vectors u and u2 with regard to the standard basis in order to determine the transition matrix from the basis u, u2 to the standard basis e1, e2.

Since u = (3,1) and u2 = (3,-1), we have

[u]e = | 3 | [u2]e = | 3 |

| 1 | |-1|

Hence, the transition matrix P from {u, u2} to {e1, e2} is

P = [u u2]e = | 3 3 |

| 1 -1 |

(b) To find the matrix representation of L with respect to {u, u2}, we need to find the coordinates of L(u) and L(u2) with respect to the basis {u, u2}. We have

L(u) = (-2)(3,1) + (2)(3,-1) = (0,-4)

L(u2) = (-6)(3,1) + (5)(3,-1) = (-3,-3)

Therefore, the matrix representation of L with respect to {u, u2} is

[L]u = | 0 -3 |

|-4 -3 |

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BC=DE are congruent and the angles are also congruent by using CPCT.

To prove BC=DE given angle BAC=angle DAE, we can use the following steps:

Draw the circle with centre A and points B, C, D, and E on its circumference.

Draw the line segment AE, and extend it to intersect the circle at point F.

Draw the line segment BF, and extend it to intersect the circle at point G.

Draw the line segments CG and DG.

Since angles BAC and DAE are equal, we have angle BAF = angle DAF (because they are vertical angles).

Since angles BAF and BGF subtend the same arc, we have angle BAF = angle BGF.

Similarly, since angles DAF and DGF subtend the same arc, we have angle DAF = angle DGF.

Since angles BGF and DGF are both equal to angle BAC/2 + angle DAE/2, we have angle BGF = angle DGF.

Since angles BGC and DGC are both equal to angle BGF + angle CGF, we have angle BGC = angle DGC.

Since angles BDC and EDC are both equal to angle CGD, we have angle BDC = angle EDC.

Therefore, BC = BG + GC = DG + GC = DE, as desired.

To prove angle BAC=angle DAE given BC=DE, we can use the following steps:

Draw the circle with centre A and points B, C, D, and E on its circumference.

Draw the line segments AC and AD.

Draw the perpendicular bisectors of BC and DE, and let them intersect at point O.

Since BC=DE, the perpendicular bisectors of BC and DE are the same line.

Therefore, point O lies on both the perpendicular bisectors of BC and DE.

Since point O lies on the perpendicular bisector of BC, we have OB = OC.

Similarly, since point O lies on the perpendicular bisector of DE, we have OD = OE.

Since OA is a radius of the circle, we have OB = OD.

Therefore, OB = OC = OD = OE, so quadrilateral BCDE is a kite.

Since a kite has two pairs of equal adjacent angles, we have angle BOC = angle DOE and angle BCO = angle EDO.

Therefore, angle BAC = angle BOC - angle BCO = angle DOE - angle EDO = angle DAE, as desired.

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According to given ratios, the inventory turnover for 20Y7 is 4.83 and the inventory turnover for 20Y6 is 5.30.

What is  ratio?

A ratio is a mathematical comparison between two or more quantities. It expresses the relationship between the two quantities by dividing one quantity by the other.

Inventory turnover is a financial ratio that measures how many times a company sells and replaces its inventory over a period of time. It is calculated by dividing the cost of goods sold by the average inventory for the period.

a. To determine the inventory turnover for 20Y7 and 20Y6, we first need to calculate the average inventory for each year:

Average inventory = (Beginning inventory + Ending inventory) / 2

For 20Y7:

Average inventory = ($770,000 + $840,000) / 2 = $805,000

For 20Y6:

Average inventory = ($740,000 + $770,000) / 2 = $755,000

Next, we can calculate the inventory turnover for each year:

Inventory turnover 20Y7 = Cost of goods sold / Average inventory 20Y7

= $3,894,000 / $805,000

= 4.83

Inventory turnover 20Y6 = Cost of goods sold / Average inventory 20Y6

= $4,001,500 / $755,000

= 5.30

Therefore, the inventory turnover for 20Y7 is 4.83 and the inventory turnover for 20Y6 is 5.30.

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Answer: See attached for a graph. 13 units apart.

Step-by-step explanation:

      See attached for a graph. We will plot the first point -8 units left and 7 units up. Then we will plot the second point 5 units right and 7 units up.

      Since these points are on a line (they both have the same y-value), we will add the absolute value of their x-values together. We can also count on the graph, you will get the same answer.

|-8| + |5| = 8 + 5 = 13

             They are 13 units apart.

Justification for equation 23x−13=2(x+2) with Distributive Property, Addition or Subtraction Property of Equality, and Division Property of Equality. We also combined and isolated variable. The final solution is x = -1.1905.

Here is a step-by-step justification for each step in the solution of the equation 23x−13=2(x+2):

Step 1: Given

The equation 23x−13=2(x+2) is given as part of the problem statement.

Step 2: Distributive Property

We distribute the 2 on the right side of the equation by multiplying it by both terms inside the parentheses to get 2x + 4. This results in the equation 23x − 13 = 2x + 4.

Step 3: Combine like terms

We combine the like terms on the right side of the equation to get 6x + 12. This results in the equation 23x − 13 = 6x + 12.

Step 4: Distributive Property

We subtract 2x from both sides of the equation to isolate the variable on one side. This results in the equation 21x - 13 = 12.

Step 5: Addition or Subtraction Property of Equality

We add 13 to both sides of the equation to isolate the variable. This results in the equation 21x = 25.

Step 6: Division Property of Equality

We divide both sides of the equation by 21 to solve for x. This results in the solution x = 25/21 or x = -1.1905.

In conclusion, the Distributive Property, Addition or Subtraction Property of Equality, and Division Property of Equality were used to support each step in the solution of the problem 23x13=2(x+2). In order to make the equation simpler and isolate the variable on one side, we additionally combined like terms. x = -1.1905 is the solution's final form.

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Find the difference between year 4 and year 5 salary.

[tex]32,625 - 31,900 = 725[/tex] (rate of change)

Multiply [tex]4 \times 725[/tex] then subtract that number from 31,900 to find out base salary

[tex]4\times 724 = 2,900[/tex]

[tex]31,900 - 2,900 = 29,000[/tex]

That's the constant.

So,

[tex]f(n) = 725n + 29,000[/tex]

The angle of 2 = (7x+13) is  ∠1 = 146°,  ∠2= 34°, ∠3 =34° ∠4= 146°

and angle 8 = (10x-44) is  ∠5 =146°, ∠6= 34°, ∠7 = 34°, ∠8= 146°

An angle is a figure obtained from two lines or rays that have the same termination in plane geometry. The common terminal of the two rays is known as the vertex.

In the given question, ∠8= ∠5 = 10x-44

∠1=7x+13

As the corresponding angles on the same side of transversal are equal,

10x-44 = 7x+13

3x = 57

x = 19

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Final outcome is: 1 quart, 2 cups. 2 quarts, 1 pint, and 2 cups are the outcome of removing 1 quart, 2 pints, and 1 cup from 3 quarts and 1 pint.

We must convert all the units to the same level of measurement in order to remove these two mixed volume units. We are aware that 2 pints and 2 cups equal 1 quart. In order to subtract the volumes, we can convert the pint and cup units to quarts.

We begin by converting 1 pint to quarts:

Pints equal half quarts.

The next step is to convert 1 cup to quarts:

1/4 pint is equal to one cup.

Hence, the second mixed unit is:

1.75 quarts are equal to 1 quart, 2 pints, and 1 cup (1 + 2(1/2) + 1/4).

We may now take the volumes away:

3 quarts and a pint minus a pint, a cup, and a quart equals 3 + 1/2 minus 1.75 to 2.75 quarts.

This result can be written as a whole number of quarts plus any leftover pints and cups to return it to mixed units. Since a quart is equal to two pints, we can write:

2.75 quarts equal 2 quarts plus a half-quart.

We may convert the remaining 1/2 quart to pints because 2 cups equal 1 pint:

2 pints from a half-quart

The end result is as a result:

1 quart, 2 cups

Therefore, 2 quarts, 1 pint, and 2 cups are the outcome of removing 1 quart, 2 pints, and 1 cup from 3 quarts and 1 pint.

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Answer: 2.43082 & 20.56918

Step-by-step explanation: The two numbers with the product of -50 and the sum of 23 are the numbers in the answer box.

The equation is also a series of subtractions. The difference between 16 and 4 is 12, and then subtracting 12 from that result gives 0.

When two quantities are subtracted from one another, the difference is produced. It represents the numerical value of the distance between two values.

The question is asking to match the given equations with the corresponding estimates that have been rounded to the nearest ones place value. The options for the estimates are given on the right-hand side.

Here are the matches:

7.7 - 3.51 ≈ 4 (Quick Check)

The difference between 7.7 and 3.51 is approximately 4.

22.78 - 14.12 ≈ 9 (Quick Check)

The difference between 22.78 and 14.12 is approximately 9.

16.208 - 3.652 ≈ 12 (Intro)

The difference between 16.208 and 3.652 is approximately 12.

3.5 - 1.2 ≈ 2 (Intro)

The difference between 3.5 and 1.2 is approximately 2.

8 - 4 = 4 (Intro)

The difference is 4.

4 - 1 = 3 (Intro)

The difference is 3.

23 - 14 - 9 (Done)

This equation is not a subtraction. It is a series of subtractions. The difference between 23 and 14 is 9, and then subtracting 9 from that result gives 0.

16 - 4 - 12 (Done)

This equation is also a series of subtractions. The difference between 16 and 4 is 12, and then subtracting 12 from that result gives 0.

Note that the terms "Quick Check" and "Intro" refer to different methods of estimation, where "Quick Check" involves rounding to the nearest ten, and "Intro" involves rounding to the nearest whole number.

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Answer:

572600

Step-by-step explanation:

572.6×1,000= 572600

And 572600 is already expressed as a decimal. Hope it helps.

Answer:

Step-by-step explanation:

I wrote two answers because I didn't understand what you meant. If there is a multiplication, then it turns out -[tex]\frac{16}{3}[/tex]≈-5,(3) or if the degree, then it will be -4

John drank 0.5025 quarts of water at the park and had 0.1675 quarts left over. It's important to note that it's always a good idea to stay hydrated, especially when spending time outdoors, and bringing enough water is key to staying hydrated.

How to solve fraction?

John brought 2/3 quart of water to the park, which can also be expressed as 0.67 quarts. If he drank 3/4 of the water he brought, this means he consumed 0.75 * 0.67 = 0.5025 quarts of water.

To verify this, we can also subtract the amount of water John drank from the amount he brought:

0.67 - 0.5025 = 0.1675 quarts

This means that John had 0.1675 quarts of water left after he drank 3/4 of what he brought.

To summarize, John drank 0.5025 quarts of water at the park and had 0.1675 quarts left over. It's important to note that it's always a good idea to stay hydrated, especially when spending time outdoors, and bringing enough water is key to staying hydrated.

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James should run along the shore for approximately 16.667 meters before jumping into the water to reach the child in the shortest possible time.

Let's call the distance James should run along the shore "x". Then, using the Pythagorean theorem, we can set up the following equation to represent the total distance James will travel to reach the child:

Simplifying and solving for x, we get:

Therefore, James should run along the shore for approximately 16.667 meters before jumping into the water to reach the child in the shortest possible time.

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Answer:

Step-by-step explanation:

about 61

Step-by-step explanation:

1.

a. ∠ADC = 40° + 30° = 70°

b. ∠DBC = 45° (given)

c. ∠AEB (reflex) = 80° + 100° + 80° = 260° (a reflex angle has to be less than 360° and greater than 180°)

d. ∠BCD = 50° + 50° = 100°

.

2.

a. I added 2 photos of my drawings

b. 47° - acute (less than 90°)

147° - obtuse (greater than 90°, less than 180°)

247° - reflex (greater than 180°, less than 360°)

347° - reflex (greater than 180°, less than 360°)

.

3.

a.The sum of the triangle's angles is equal to 180°

i. 180° - 45° - 75° = 60°

ii. 180° - 8° - 11° = 161°

iii. 180° - 54° - 54° = 72°

iv. 180° - 138° - 21° = 21°

b. The third and the fourth, because they have two identical angles

.

4.

Quadrilateral's sum of angles is equal to 360°

a. 360° - 72° - 97° - 113° = 78°

b. 360° - 55° - 55° - 155° = 95°

c. 360° - 77° - 77° - 77° = 129°

.

5. a. No, because then they won't form a total of 360°, since each of them is greater than 90°

b. Yes, because then they would form a total of 360° (the fourth angle must be acute)

c. Yes, because it would still be possible for the sum of quadrilateral's angles to be 360° (the remaining 3 angles must be acute)

d. No, because 2 reflex angles would already form a minimum of 360° (or even more), that has to be the sum of 4 angles, so it wouldn't be possible for a quadrilateral to have only 2 angles

Answer:

On a number line, the solution x = -10 would be located to the left of the origin (0) by a distance of 10 units. So, you would mark the point representing -10 on the number line to the left of 0.

Step-by-step explanation:

csc(x) = 1/sin(x)

We know that sin(-x) = -sin(x), so we can rewrite csc(-176°) as:

csc(-176°) = 1/sin(-176°) = -1/sin(176°)

Now, we need to find sin(176°) without a calculator. We can use the fact that the sine function has period 360°:

sin(x) = sin(x - 360°)

Therefore, we can subtract 360° from 176° until we get an angle between 0° and 360°:

176° - 360° = -184° + 360° = 176° - 360° = -184° + 360° = ...

We can continue this process until we get an angle between 0° and 360°. Notice that after each subtraction of 360°, the sine function is negated:

sin(176°) = -sin(-184°) = sin(176° - 360°) = -sin(-184° + 360°) = ...

We can continue this process until we get an angle between 0° and 360°:

sin(176°) = -sin(-184°) = sin(176° - 360°) = -sin(-184° + 360°) = sin(176° - 720°) = -sin(-544°) = sin(544°)

Now, we need to find the sine of 544°, which is equivalent to the sine of 544° - 360° - 360° = -176°. We know that sin(-x) = -sin(x), so:

sin(544°) = -sin(-176°) = sin(176°)

Therefore:

csc(-176°) = -1/sin(176°)

Now, we can use the fact that sin^2(x) + cos^2(x) = 1 to find cos(176°):

sin^2(176°) + cos^2(176°) = 1

cos^2(176°) = 1 - sin^2(176°)

cos(176°) = ±sqrt(1 - sin^2(176°))

Since 0° ≤ 176° ≤ 180°, the cosine function is negative:

cos(176°) = -sqrt(1 - sin^2(176°))

Substituting this into the formula for csc(-176°), we get:

csc(-176°) = -1/sin(176°) = -1/(-sqrt(1 - cos^2(176°))) ≈ -17.204

Therefore, the value of csc(-176°) to the nearest thousandth is -17.204.

Answer:

it's the 4th graph and for the second one it's vertical shrink by 1/4

Answer:

The ratio of the number of votes in favor of the law to the total number of votes is:

14 (votes in favor of the law) : 50 (total number of votes)

This ratio can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 2:

7 (votes in favor of the law) : 25 (total number of votes)

So the ratio of votes in favor of the law to the total number of votes is 7:25.

The function model and the population of water buffalo is

[tex]P_{current} = P_{estimated} \left(1-\frac{R}{100} \right)^t[/tex]

How to find the population function of decreasing at a certain rate?

Let assume some variable of population and rate change,

 [tex]P_{estimated} = Estimated\ population\ of\ water\ buffalo\\R = Rate\ of\ decreasing\ population\ of\ water\ buffalo\\t = time\ taken\ for\ decrease\\[/tex]

Therefore, the function for population of water buffalo decreasing, using compound interest is

[tex]P_{current} = P_{estimated} \left(1-\frac{R}{100} \right)^t[/tex]

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Answer:

120ft²

Step-by-step explanation:

SA = 6(8) + (6+8+10) 3

= 48 + (24)(3)

= 48 + 72

= 120ft²

The argument that there's a direct association between the two variables is sufficiently supported by the available data.

The graphs that show the association between two variables in a data set are called smatter plots. It displays data points moreover on a Cartesian system or a two- dimensional aeroplane

. TheX-axis is used to represent the independent variable or trait, while the Y- axis is used to compass the dependent variable. These plates or graphs are constantly used to describe these plots.

Measure of direct correlation. The strength of the direct link between two variables, x and y, is shown by a number known as the direct correlation measure, which is deduced from given data. The direction of the direct link between x and y is indicated by the sign of the direct correlation measure.

Given,

x y

109.14

88.15

138.75

98.77

119.25

148.09

66.13

43.09

129.14

77.25

54.73

r=0.81602411

therefore correlation measure is0.816 a strong positive correlation.

Test statistic t =

p value<0.05 our significant position

Hence reject H0, there's correlation significant between the two variables.

There's sufficient substantiation to support the claim of a direct correlation between the two variables

smatter plot is attached.

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The value of the variable in the circle is x = 4.5.

If two secant segments shares an endpoint outside of the circle. The product of one secant segment and its external segment is equal to the product of the other secant segment and its external segment.

In this case, Use the theorem above, we can say:

5 * 18 = x * 20

90 = 20x

x = 90/20

x = 4.5

Thus, the value of the variable is x = 4.5.

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Answer:

x=1, x=15

Step-by-step explanation:

[tex]x^2+16x=-15\\x^2+16x+(8)^2=-15+8^2\\x^2+16x+64=-15+64\\(x+8)^2=49\\\sqrt{(x+8)^2=49} \\x+8=+-7\\x=8-7 = 1\\x=8+7=15[/tex]

Answer: We can use the fact that the sine function is an odd function, which means that:

sin(-x) = -sin(x)

So, we have:

sin(-15 degrees) = -sin(15 degrees)

We can use the sum and difference identity for sine, which states that:

sin(a - b) = sin(a)cos(b) - cos(a)sin(b)

Letting a = 45 degrees and b = 30 degrees, we get:

sin(45 degrees - 30 degrees) = sin(45 degrees)cos(30 degrees) - cos(45 degrees)sin(30 degrees)

We can use the fact that cos(45 degrees) = sin(45 degrees) = √2 / 2 and cos(30 degrees) = √3 / 2 and sin(30 degrees) = 1 / 2 to simplify:

sin(15 degrees) = (√2 / 2)(√3 / 2) - (√2 / 2)(1 / 2)

sin(15 degrees) = (√6 - √2) / 4

Therefore, we have:

sin(-15 degrees) = -sin(15 degrees) = -[(√6 - √2) / 4] = (-√6 + √2) / 4

So the exact value of sin(-15 degrees) is (-√6 + √2) / 4.

Step-by-step explanation: